1. Field of the Invention
The present invention relates to a method for determining the resistivity index RI, as a function of the water saturation, of certain rocks of complex porosity.
2. Description of the Prior Art
Evaluation of carbonate reservoirs is a particularly difficult task for petrophysicists, who still lack precise knowledge concerning the carrying properties within these porous media. In relation to siliclastic rocks, carbonates may be simpler on the mineralogical plane, but they are incomparably more complex in terms of pore structure and surface properties. The largely biological origin of the sediments, combined with various diagenetic processes, leads to complex pore structures that may be very different from one reservoir to the next. For many carbonate systems, resistivity data calibrations carried out in the laboratory contradict the observations made in the field (anhydrous production, capillary pressure) and the direct water saturation measurements performed on preserved cores.
The prior art is notably defined by the following publications:                Bouvier L. et al., Reconciliation of Log and Laboratory Derived Irreducible Water Saturation in a Double Porosity Reservoir, Advances in Core Evaluation, edited by Worthington and Longeron, Gordon and Breach Science Publishers,        Dixon J. R. et al. (1990), The Effect of Bimodal Pore Size Distribution on Electrical Properties of some Middle Eastern Limestone, Soc. Petr. Eng. 20601, 7th SPE Middle Eastern Oil Show, Bahrain, pp.743-750,        Fleury M. (1998), “FRIM: a Fast Resistivity Index Measurement Method”, Proceedings of the International Symposium of the Society of the Core Analysts, Den Hague,        Fleury M. et al. (2000) “Frequency Effect on Resistivity Index Curves Using a New Method”, Proceedings of the 41st Annual SPWLA Symposium, Dallas,        Moore C. H. (2001) “Carbonate Reservoirs, Porosity Evaluation and Diagenesis in a Sequence Stratigraphic Framework”, Developments in Sedimentology 55, Elsevier Editions,        Petricola M. J. C. et al. (1995) “Effect of Microporosity in Carbonates: Introduction of a Versatile Saturation Equation”, Soc. Petr. Eng. 29841, SPE Middle Eastern Oil Show, Bahrain, pp.607-615,        Sen P. N. et al. (1997) “Resistivity of Partially Saturated Rocks with Microporosity”, Geophysics, Vol.62, No.2, pp415-425.        
Understanding and prediction of the effect of the structure of the pore network, of the wettability and of the electrical properties of carbone rocks is a real scientific challenge, theoretically as well as experimentally. In fact, correct evaluation of these parameters has a major impact on estimation of the oil in place, notably for Middle Eastern giant fields, because the difference in relation to the standard values of Archie's exponents m and n in relation to value 2 is so great that estimation of the water saturation can vary by more than 20%.
Various experimental observations have shown the existence of distinct pore populations: micropores, macropores and mesopores, with different coexistence degrees. In general, the resistivity index curve RI(Sw)=Rt(Sw)/Ro, where Rt is the resistivity of the rock to a water saturation Sw, and Ro the resistivity for Sw=1, cannot be described by a power law (second Archie's law RI=Sw−n), that is n is a function of the saturation itself. Microporosity can act as a parallel path for the current, which leads to a decrease in the values of n and, therefore, to a gradual insensitivity of the resistivity to saturation, as observed on clayey sands. Microporosity can also be the cause of the low measured values of n (typically 1.45). It has also been observed that n can increase considerably under certain conditions, and there might be a connection between curve RI(Sw) and the capillary pressure curve. The increase in the values of n is also a known effect of the wettability, which tends to favor aqueous phase discontinuity and therefore to increase the resistivity to water wettability. The effect of the wettability can lead to either a sudden increase of n, or to a high value n without discontinuity, which can lead to confusion.
The experimental curves RI(Sw) which have been drawn from various prior works, already mentioned above, and from observations can have (FIG. 1) four distinct shapes which do not always meet Archie's laws:                type I: can be typical of carbonates from the Thamama formation,        type II: straightens at intermediate saturation and flattens at low saturation (present study),        type III: single slope at low saturation, extrapolation at Sw=1 above Ir=1, and        type IV: typical of oil-wet systems, high values of n that can increase further at low saturation. This is also valid for clasts.        
It can thus be seen that, in the presence of rocks of complex porosity which do not meet Archie's laws, a large number of costly measurements is necessary to take account of the variability of the pore structure.